It is interesting to note that contrary to works from classical robust theory from the 70's, the influence functions of the M-estimators used by Catoni are not necessarily bounded. In this article, we initiate the analysis of the effect of unbounded influence function on the robustness of M-estimators, Huber [1]} told us that the influence function must be bounded while Catoni uses unbounded influence function and he still shows robust properties for this type of estimator, the difference is in their vision of what is a robust estimator.
